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Suppose we have a binary classifer that always chooses 0 no matter what. In this case, the ROC curve will be a horizontal line with AUC equal to 0.5. My question is, if we have such a curve, does it even make sense in that we only have two data points (one at (1,1), and one at (0,0))? Since no data can go in the middle empirically why are we allowed to connect the two points using a line?

user321627
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    It's not clear to me that always outputting 0 will lead to the ROC you describe. – gung - Reinstate Monica Oct 24 '17 at 02:04
  • https://stats.stackexchange.com/questions/132777/what-does-auc-stand-for-and-what-is-it – julian Oct 24 '17 at 02:10
  • You seem to be describing two lines. Is horizontal a typo for straight? – mdewey Oct 24 '17 at 08:15
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    Your premise is wrong. Sensitivity will always be 0 (no true positive), and specificity = 1 (no false positive). Hence you have a single point in the ROC space only (at (0,0)), not two. No curve, no AUC. – Calimo Oct 24 '17 at 09:16

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Sure, you can probably connect the points but to what would that buy you? It sounds like your model fits poorly (or not at all). I'd look more closely at the model before interpreting an ROC where AUC == 0.5

HEITZ
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